Monday, July 1, 2019

The metaphysical conceit, associated with the Metaphysical poets of the 17th century, is a more intricate and intellectual device. It usually sets up an analogy between one entity's spiritual qualities and an object in the physical world and sometimes controls the whole structure of the poem.…

Thursday, June 23, 2016

Breaking the Code of the Archetypal Self:An Introductory Overview of the Research Discoveries
Leading to Neo-Jungian Structural Psychoanalysis

Dr. Moore will introduce his research and discoveries
with regard to the deep structures of the Self.
Tracing the foundations in the tradition of Jung’s
affirmation of the collective unconscious, Moore
will present his “decoding of the Diamond Body,”
a mapping of the deep structures of the Great Code
of the psyche. . . .

Googling "Jung" + "Diamond Body" shows that
Moore's terminology differs from Jung's.
The octahedron that Moore apparently associates
with his "diamond body" was discussed by Jung
in a different context. See selections from Ch. 14
of Jung's Aion: "The Structure and Dynamics of the Self."

"'… Think of a match. You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released. Friction does it. But when Meta excites and releases energy, it's like a stick of dynamite compared to a match. It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah. The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what. The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

Saturday, May 19, 2012

Here is a link to a copy of the home page of a Turkish
author quoted here on May 4, 2012… in honor of
archaeologist Crawford Greenewalt Jr., who reportedly
died on that date. Greenewalt was an expert on the
ancient city of Sardis, in what is now western Turkey.

A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar—

1. User Submissions. "… you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."

Max Black — "Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as 'three in one' should be child's play." ("The Elusiveness of Sets," Review of Metaphysics, June 1971, p. 615– as quoted by Bill Vallicella)

The above figure shows how four-part partitions
of the 16 vertices of a tesseract in an infiniteEuclidean space are related to four-part partitions
of the 16 points in a finite Galois space

Euclidean spaces versus Galois spaces
in a larger context—

Infinite versus Finite

The central aim of Western religion —

"Each of us has something to offer the Creator...
the bridging of
masculine and feminine,
life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy —

Dualities of Pythagoras
as reconstructed by Aristotle:
Limited Unlimited
Odd Even
Male Female
Light Dark
Straight Curved
... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in The Music of the Spheres (1993)

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science… reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896).

Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—

… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect.

Who can pick up the weight of Britain,
Who can move the German load
Or say to the French here is France again?
Imago. Imago. Imago.
It is nothing, no great thing, nor man
Of ten brilliancies of battered gold
And fortunate stone. It moves its parade
Of motions in the mind and heart,
A gorgeous fortitude. Medium man
In February hears the imagination's hymns
And sees its images, its motions
And multitudes of motions
And feels the imagination's mercies,
In a season more than sun and south wind,
Something returning from a deeper quarter,
A glacier running through delirium,
Making this heavy rock a place,
Which is not of our lives composed . . .
Lightly and lightly, O my land,
Move lightly through the air again.

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system of points and hyperplanes from the diamond theorem. This system was depicted by artist Josefine Lyche in her installation “Theme and Variations” in Oslo in 2009. Lyche titled this part of her installation “The Smallest Perfect Universe,” a phrase used earlier by Burkard Polster to describe the projective 3-space PG(3,2) that contains these points (at right below) and hyperplanes (at left below).

Although the system of points (at right above) and hyperplanes (at left above) exemplifies Valéry’s notion of invariant, it seems unlikely to be the sort of thing he had in mind as an image of the Self.

“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”

“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness….”

The NY evening number, 091, may be viewed as a followup to the NY midday 378 (the number of pages in The Innermost Kernel by Suzanne Gieser, published by Springer, 2005)–

Page 91: The entire page is devoted to the title of the book's Part 3– "The Copenhagen School and Psychology"–

The next page begins: "With the crisis of physics, interest in epistemological and psychological questions grew among many theoretical physicists. This interest was particularly marked in the circle around Niels Bohr."

The circle above is
marked with a version of
the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.
"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."
-- Wallace Stevens,
"Notes Toward a Supreme Fiction,"
Canto IV of "It Must Change"
The square above is marked
with a graphic design
related to the four-diamond
figure of Jung's Aion.

"From the circle and quaternity motif is derived the symbol of the geometrically formed crystal and the wonder-working stone. From here analogy formation leads on to the city, castle, church, house, room, and vessel. Another variant is the wheel. The former motif emphasizes the ego’s containment in the greater dimension of the self; the latter emphasizes the rotation which also appears as a ritual circumambulation. Psychologically, it denotes concentration on and preoccupation with a centre…." –Jung, Collected Works, Vol. 9, Part II, paragraph 352

As for rotation, see the ambigrams in Dan Brown's Angels & Demons (to appear as a film May 15) and the following figures:

They fall well. With a sort of panache. They plume down in their last Loveliness, disguising their fear Of being dried and pounded to ash To mix with the common dust. They go in grace, making their fall appear Like flying.ROXANE You’re melancholy today.CYRANO Never. I’m not the melancholy sort.ROXANE Very well, then. We’ll let The leaves of the fall fall while you Turn the leaves of my gazette. What’s new at court?CYRANO … There have been some scandals To do with witches. A bishop went to heaven, Or so it’s believed: there’s been as yet no report Of his arrival….”

Later….

CYRANO … See it there, a white plume Over the battle– A diamond in the ash Of the ultimate combustion– My panache.”

Tuesday, January 6, 2009

The current (Feb. 2009) Notices of the American Mathematical Society has a written version of Freeman Dyson’s 2008 Einstein Lecture, which was to have been given in October but had to be canceled. Dyson paraphrases a mathematician on Carl Jung’s theory of archetypes:

“… we do not need to accept Jung’s theory as true in order to find it illuminating.”

“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”

For related thoughts by Jung,see Aion, which contains thefollowing diagram:

“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity.”

— Carl Gustav Jung

That the words Maximus of Tyre (second century A.D.) attributed to Heraclitus imply a cycle of the elements (analogous to the rotation in Jung’s diagram) is not a new concept. For further details, see “The Rotation of the Elements,” a 1995 webpage by one “John Opsopaus.”

"'… Think of a match. You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released. Friction does it. But when Meta excites and releases energy, it's like a stick of dynamite compared to a match. It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah. The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what. The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”

“The formula presents a symbol of the self, for the self is not just a stable quantity or constant form, but is also a dynamic process. In the same way, the ancients saw the imago Dei in man not as a mere imprint, as a sort of lifeless, stereotyped impression, but as an active force…. The four transformations represent a process of restoration or rejuvenation taking place, as it were, inside the self….”

“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity.

What the formula can only hint at, however, is the higher plane that is reached through the process of transformation and integration. The ‘sublimation’ or progress or qualitative change consists in an unfolding of totality into four parts four times, which means nothing less than its becoming conscious. When psychic contents are split up into four aspects, it means that they have been subjected to discrimination by the four orienting functions of consciousness. Only the production of these four aspects makes a total description possible. The process depicted by our formula changes the originally unconscious totality into a conscious one.”

“Although ‘wholeness’ seems at first sight to be nothing but an abstract idea (like anima and animus), it is nevertheless empirical in so far as it is anticipated by the psyche in the form of spontaneous or autonomous symbols. These are the quaternity or mandala symbols, which occur not only in the dreams of modern people who have never heard of them, but are widely disseminated in the historical recods of many peoples and many epochs. Their significance as symbols of unity and totality is amply confirmed by history as well as by empirical psychology. What at first looks like an abstract idea stands in reality for something that exists and can be experienced, that demonstrates its a priori presence spontaneously. Wholeness is thus an objective factor that confronts the subject independently of him… Unity and totality stand at the highest point on the scale of objective values because their symbols can no longer be distinguished from the imago Dei. Hence all statements about the God-image apply also to the empirical symbols of totality.”

Doxiadis is describing how talks by two noted mathematicians were related to

"… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "

Doxiadis says both talks had "a big hole in the middle."

"Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts. [In one part] I’ll tell you a few things about proofs. [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
"And the hole?""This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’ But the similarity was not clearly explained: the hole, you see, the ‘miracle.’ Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."

Part II: Possible Worlds

"At times, bullshit can only be countered with superior bullshit."
— Norman Mailer

"The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. Voltaire satirized this view in his picaresque novel Candide….
Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
– Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)

"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
– Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)

"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
– The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)

"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."

Friday, February 20, 2004

The protagonist of the recent bestseller The Da Vinci Code is Robert Langdon, "a professor of Religious Symbology at Harvard University." A prominent part in the novel is played by the well-known Catholic organization Opus Dei. Less well known (indeed, like Langdon, nonexistent) is the academic discipline of "symbology." (For related disciplines that do exist, click here.) What might a course in this subject at Harvard be like?

While Opus Dei members said that they do not refer to their practices of recruitment as "fishing," the Work’s founder does describe the process of what he calls "winning new apostles" with an aquatic metaphor.

Point #978 of The Way invokes a passage in the New Testament in which Jesus tells Peter that he will make him a "fisher of men." The point reads:

" ‘Follow me, and I will make you into fishers of men.’ Not without reason does our Lord use these words: men—like fish—have to be caught by the head. What evangelical depth there is in the ‘intellectual apostolate!’ ”

Exercise for Symbology 101:

Describe the symmetry
in each of the pictures above.
Show that the second picture
retains its underlying structural
symmetry under a group of
322,560 transformations.

Having reviewed yesterday's notes
on Gombrich, Gadamer, and Panofsky,
discuss the astrological meaning of
the above symbols in light of
today's date, February 20.

Extra credit:

Relate the above astrological
symbolism to the four-diamond
symbol in Jung's Aion.